Question: Simplify to lowest terms. $\dfrac{72}{80}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 80? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $80 = 2\cdot2\cdot2\cdot2\cdot5$ $\mbox{GCD}(72, 80) = 2\cdot2\cdot2 = 8$ $\dfrac{72}{80} = \dfrac{9 \cdot 8}{ 10\cdot 8}$ $\hphantom{\dfrac{72}{80}} = \dfrac{9}{10} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{72}{80}} = \dfrac{9}{10} \cdot 1$ $\hphantom{\dfrac{72}{80}} = \dfrac{9}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{80}= \dfrac{2\cdot36}{2\cdot40}= \dfrac{2\cdot 2\cdot18}{2\cdot 2\cdot20}= \dfrac{2\cdot 2\cdot 2\cdot9}{2\cdot 2\cdot 2\cdot10}= \dfrac{9}{10}$